Mean-Field Approximations With Adaptive Coupling for Networks With Spike-Timing-Dependent Plasticity

Area of Science:

• Computational Neuroscience
• Neural Dynamics
• Complex Systems

Background:

• Spike-timing-dependent plasticity (STDP) is crucial for understanding neural network adaptation but computationally expensive.
• Existing models lack low-dimensional descriptions for analytical insights into long-term neural changes.
• Phase-difference-dependent plasticity (PDDP) offers an approximation for STDP in phase oscillator networks.

Purpose of the Study:

• To develop mean-field approximations for phase oscillator networks with STDP.
• To provide low-dimensional descriptions of adaptive neural networks.
• To inform the design of interventions for neurological disorders using insights from neural plasticity.

Main Methods:

• Constructed mean-field approximations for phase oscillator networks incorporating STDP.
• Investigated single-harmonic and multi-harmonic PDDP rules for approximating symmetric and causal STDP.
• Derived exact expressions for average PDDP coupling weight evolution based on network synchrony.
• Formulated low-dimensional descriptions for adaptive Kuramoto oscillator networks forming clusters.

Main Results:

• Single-harmonic PDDP rules approximate symmetric STDP; multi-harmonic rules are needed for causal STDP.
• Derived expressions link average PDDP coupling weight to network synchrony.
• Developed low-dimensional mean-field models for clustered adaptive oscillator networks.
• Successfully fitted a two-cluster mean-field model to synthetic data, approximating a full adaptive network with STDP.

Conclusions:

• The developed framework offers a step towards low-dimensional descriptions of adaptive networks with STDP.
• PDDP provides a computationally tractable method to study STDP effects in large neural networks.
• This approach could guide the development of therapies, such as brain stimulation, for neurological conditions.